Cluster transformations, the tetrahedron equation, and three-dimensional gauge theories

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI:10.4310/atmp.2023.v27.n4.a2
Xiaoyue Sun, Junya Yagi
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引用次数: 0

Abstract

We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three trivial cluster transformations with 8, 32 and 32 mutations. For each of these cluster transformations, a unitary operator representing a single braid move in a quantum mechanical system solves the tetrahedron equation. The solutions thus obtained are constructed from the noncompact quantum dilogarithm and can be identified with the partition functions of three-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories on a squashed three-sphere.
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簇变换、四面体方程和三维规规理论
我们定义了对称群 $S_n$ 的辫子关系通过突变和自动变形实现的三个四元组家族。在$S_4$的最长元素的缩减词上的八个辫状移动序列产生了三个具有 8、32 和 32 个突变的微不足道的簇变换。对于每一种簇变换,量子力学系统中代表单一辫状移动的单元算子都能求解四面体方程。由此得到的解是由非紧凑量子稀释算式构造的,可以与压扁三球上的三维 $mathcal{N} = 2$ 超对称规理论的分区函数相鉴别。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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